Statistical Methods And Calculation Skills

Front cover......Page 1
Title page......Page 2
Imprint page......Page 3
Table of contents......Page 4
Part 1: Statistical methods......Page 8
Unit 1: Introduction......Page 10
1.1 Problem-solving steps......Page 11
1.2 Definition......Page 12
1.3 The language of statistics......Page 13
1.4 Measurement......Page 14
1.4.3 Interval scale......Page 15
1.4.4 Ratio scale......Page 16
1.5 Role of the computer in statistics......Page 17
2.1 Sources of data: where to get the data......Page 22
2.2 Primary data sources......Page 23
2.2.2 Observations......Page 24
2.2.4 Survey by means of asking questions......Page 25
2.3.3 Types of questions we can ask......Page 27
2.4 Selecting a sample......Page 28
2.4.3 Sampling error......Page 29
2.5 Non-random or non-probability sampling methods......Page 30
2.5.4 Snowball sampling......Page 31
2.6.1 Simple random sampling......Page 32
2.6.4 Cluster sampling......Page 34
Unit 3: Summarising data using tables and graphs......Page 36
3.1.1 Frequency distributions......Page 37
3.1.2 Cross-tabulation......Page 39
3.1.3 Bar graph for a single data set......Page 40
3.1.4 Comparative bar graphs......Page 42
3.1.5 Pie chart......Page 46
3.1.6 Pictograms......Page 47
3.2.2 Dot plot......Page 48
3.2.3 Stem-and-leaf plot......Page 50
3.2.4 Frequency distribution tables......Page 53
3.3.1 The histogram and relative histogram......Page 59
3.3.2 Polygon and relative polygon......Page 62
3.3.3 Ogive (cumulative curve) and relative ogive......Page 63
3.4 Using software......Page 65
Unit 4: Summarising data using numberical descriptors......Page 72
4.1.1 Arithmetic mean......Page 73
4.1.2 Median......Page 77
4.1.3 Mode......Page 82
4.1.4 Choose between the mean, median or mode......Page 86
4.2.1 The range......Page 88
4.2.2 Mean absolute deviation (MAD)......Page 89
4.2.3 Standard deviation......Page 92
4.2.5 Coefficient of variation......Page 96
4.3 Measures of shape......Page 97
4.3.1 Skewness......Page 98
4.3.2 Measures of kurtosis......Page 100
4.4 Interpreting centre and variability......Page 101
4.5 Measures of relative standing......Page 105
4.6.1 Interfractile ranges......Page 110
4.6.2 Quartile deviation......Page 111
4.6.3 Five-number summary table......Page 112
4.6.4 Box-and-whisker plot......Page 113
Unit 5: Index numbers......Page 120
5.1 Construction of a simple index number......Page 122
5.2 Construction of composite (or aggregate) index numbers......Page 123
5.2.1 Unweighted index numbers......Page 124
5.2.2 Weighted composite index numbers......Page 125
5.3.1 The consumer price index......Page 127
5.3.2 Changing the base year......Page 128
5.3.3 Link (or chain) indexes......Page 129
5.3.4 Percentage points change......Page 130
5.3.5 Real value versus nominal value of money......Page 131
Unit 6: Summarising bivariate data: simple regression and correlation and analysis......Page 134
6.2 Scatter diagram......Page 135
6.3 Correlation analysis......Page 138
6.3.2 Interpreting a correlation coefficient......Page 139
6.3.3 The coefficient of determination......Page 140
6.4.1 Formulating the regression equation......Page 141
6.4.3 Plot the regression line on the scatter diagram......Page 142
6.5 Spearman rank correlation coefficient......Page 145
7.1 Components of a time series......Page 152
7.2 Historigram......Page 154
7.3.1 Trend analysis......Page 155
7.3.2 Seasonal variation......Page 163
Unit 8: Probability: basic concepts......Page 174
8.1 Language of probability......Page 175
8.2.1 Classical approach......Page 176
8.2.2 Empirical probability......Page 177
8.2.3 Subjective probability approach......Page 178
8.3 Properties of probabilities......Page 179
8.4.2 Intersection of two events......Page 181
8.4.3 Display events graphically......Page 182
8.5 Probability rules for compound events......Page 184
8.5.1 Addition rules......Page 185
8.5.2 Multiplication rules......Page 187
8.5.3 Calculating probabilities using a contingency table......Page 190
8.5.4 Tree diagrams......Page 192
8.6.1 Multiplication rule of counting......Page 194
8.6.3 Combination rule......Page 195
Unit 9: Probability distribution......Page 204
9.1 Discrete probability distributions......Page 205
9.1.1 The binomial distribution......Page 206
9.1.2 Poisson distribution......Page 208
9.2.1 The normal distribution......Page 210
9.2.2 Different areas under the normal curve......Page 212
10.1 Statistics and pa rameters......Page 222
10.2 Sampling distribution of the means......Page 223
10.3.1 Point estimation......Page 224
10.3.2 Confidence interval estimates......Page 225
10.3.3 Confidence interval estimate for the population mean (μ) fordata obtained from a population that is normally distributed or from large samples......Page 228
10.3.4 Confidence interval estimate for the population mean using small samples with σ unknown: t distribution......Page 229
10.3.5 Confidence interval estimate for the population proportion......Page 230
10.4 Sample size......Page 231
Unit 11: Hypothesis testing......Page 236
11.1.1 Stating the hypotheses......Page 237
11.1.2 Select a level of significance (α) to be used......Page 238
11.1.4 Determine the critical value(s) and identify the rejection region......Page 239
11.1.5 Conduct the statistical test......Page 241
11.1.7 Interpret the decision......Page 242
11.2 Hypothesis testing using the P value approach......Page 246
11.3 Testing the difference among means and proportions......Page 249
11.4.1 Test for independence......Page 253
11.4.2 Goodness-of-fit tests......Page 256
Part 2: Calculation skills......Page 266
12.1 The electronic calculator......Page 268
12.2.2 Real numbers and imaginary numbers......Page 270
12.2.3 Rational numbers and irrational numbers......Page 271
12.2.4 Whole numbers and fractions......Page 272
12.3 Common notation......Page 273
12.4.2 Adding and subtracting......Page 274
12.4.3 Multiplying and dividing......Page 275
12.5 Signed numbers......Page 277
12.7 Square roots......Page 278
12.9 Factorial notation......Page 279
12.10 Sigma notation......Page 280
12.11 Fractions......Page 281
12.12 Decimal numbers......Page 283
12.13 Scientific notation......Page 284
12.14 Rounding off decimals......Page 285
12.15 Significant digits......Page 287
12.16 The metric system......Page 290
13.1.1 Converting percentages to fractions and decimals......Page 292
13.1.2 Converting a fraction or decimal into a percentage......Page 293
13.1.4 Finding the rate......Page 294
13.1.6 Percentage rate increase or decrease......Page 295
13.1.7 Finding the amount......Page 296
13.2 Ratio (proportion) calculation......Page 297
13.3.1 Mark-up on cost price......Page 298
13.3.2 Mark-downs and discounts......Page 299
13.3.3 Value-added tax calculations......Page 300
14.1 Graph construction......Page 304
14.2.2 Linear cost function......Page 306
14.2.4 Linear profit function......Page 308
14.2.5 Break-even analysis......Page 309
15.1 Basic concepts......Page 312
15.2 Simple interest......Page 313
15.3 Compound interest......Page 314
15.5 Annuities......Page 317
15.5.1 Ordinary annuities certain......Page 318
15.5.2 Ordinary annuities due......Page 320
Appendix 1......Page 325
Appendix 2......Page 326
Appendix 3......Page 327
Appendix 4......Page 328